Solve graphically the following system of linear equations if it has unique solution:

2x — 3y = 1

3x — 4y = 1

The given pair of linear equations is

2x – 3y = 1 or 2x – 3y – 1 = 0

and 3x – 4y = 1 or 3x – 4y – 1 = 0

On comparing the given equations with standard form of pair of linear equations i.e. a₁ x + b₁y + c₁ = 0 and a₂ x + b₂y + c₂ = 0, we get

a₁ = 2, b₁ = – 3 and c₁ = – 1

and a_{2 =} 3, b₂ = – 4 and c₂ = – 1

The lines representing the given pair of linear equations will intersect at a point.

Now, table for or

Now, table for or

Here, the lines intersecting at point C i.e. ( – 1, – 1)

Hence, the unique solution is x = – 1 and y = – 1.